| Abstract: | Through an energy formulation and the use of a large deflection theory, it is shown that if a thin plate has a slight initial preform, and if its edges are constrained against in–plane displacements, then all of the natural frequencies of the plate will be shifted upward. For a uniform thin plate, the amount of frequency shift depends on the type of boundary conditions and the ratio of the amplitude of preform to the thickness of the plate. Examples of square and rectangular plates preformed in the shape of their first mode shapes are presented. The method holds the promise of shifting or essentially removing a troublesome vibration mode. |
